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Juhász, Junger Irén. "Green-function theory of anisotropic Heisenberg magnets with arbitrary spin." Doctoral thesis, Universitätsbibliothek Leipzig, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-70957.
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In this thesis, anisotropic Heisenberg magnets with arbitrary spin are investigated within the second-order Green-function theory. Three models are considered.
First, the second-order Green-fuction theory for one-dimensional and two-dimensional Heisenberg ferromagnets with arbitrary spin S in a
magnetic field is developed. For the determination of the introduced vertex parameters sum rules, higher-derivative sum rules, and regularity conditions are derived, and the equality of the isothermal and the longitudinal uniform static Kubo susceptibilities is required. Thermodynamic quantities, such as the specific heat, magnetic susceptibility, transverse and longitudinal correlation lengths are calculated. Empirical formulas describing the dependence of the position and height of the susceptibility maximum on the magnetic field are given. An anomal behavior of the longitudinal correlation length is observed. The appearance of two maxima in the temperature dependence of the specific heat is discussed.
Further, as an example of a system with an anisotropy in the spin space, the S=1 ferromagnetic chain with easy-axis single-ion anisotropy is studied. Justified by the up-down symmetry of the model with respect to $S_i^z -> -S_i^z$, $\\langle S_i^z \\rangle=0$ is set. Two different ways of the determination of the introduced vertex parameters are presented. The transverse nearest-neighbor correlation function, spin-wave spectrum and longitudinal correlation length are analyzed. The effects of the single-ion anisotropy on the transverse and longitudinal uniform static
susceptibilities as well as on the appearance of two maxima in the temperature dependence of the specific heat are examined.
Finally, as examples of spatial anisotropic spin systems,layered Heisenberg
ferromagnets and antiferromagnets with arbitrary spin are studied within the rotation-invariant Green-function theory. The long-range order is described by the condensation term, which is determined from the requirement that in the ordered state the static susceptibility has to diverge at the ordering wave vector. For determination of the introduced vertex parameters, the sum rule and the isotropy condition are used and also assumptions regarding the temperature dependence of some parameters are made. The main focus is put on the calculation of the specific heat, the Curie temperature, and the Néel temperature in dependence on the interlayer coupling and the spin-quantum number. Empirical formulas describing the dependence of the transition temperatures on the ratio of interlayer and intralayer couplings are given.
For all three models, the results of the Green-function theory are compared to available results of exact approaches (Quantum Monte Carlo, exact diagonalization, Bethe-ansatz method) and to available experimental data.
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Nyobe, Likeng Samuel Aristide. "Heisenberg Categorification and Wreath Deligne Category." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/41167.
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We define a faithful linear monoidal functor from the partition category, and hence from Deligne's category Rep(S_t), to the additive Karoubi envelope of the Heisenberg category. We show that the induced map on Grothendieck rings is injective and corresponds to the Kronecker coproduct on symmetric functions.
We then generalize the above results to any group G, the case where G is the trivial group corresponding to the case mentioned above. Thus, to every group G we associate a linear monoidal category Par(G) that we call a group partition category. We give explicit bases for the morphism spaces and also an efficient presentation of the category in terms of generators and relations. We then define an embedding of Par(G) into the group Heisenberg category associated to G. This embedding intertwines the natural actions of both categories on modules for wreath products of G. Finally, we prove that the additive Karoubi envelope of Par(G) is equivalent to a wreath product interpolating category introduced by Knop, thereby giving a simple concrete description of that category.
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Schenk, Stefan. "Density functional theory on a lattice." kostenfrei, 2009. http://d-nb.info/998385956/34.
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Wong, Ming Lai. "Q-Fourier transform, q-Heisenberg algebra and quantum group actions /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?MATH%202003%20WONG.
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Shiri-Garakani, Mohsen. "Finite Quantum Theory of the Harmonic Oscillator." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5078.
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We apply the Segal process of group simplification to the linear harmonic oscillator. The result is a
finite quantum theory with three quantum constants instead of the usual one. We compare the classical (CLHO), quantum (QLHO), and finite (FLHO) linear harmonic oscillators and their canonical or unitary groups. The FLHO is isomorphic to a
dipole rotator with N=l(l+1) states where l is very large for physically interesting case. The position and momentum variables are quantized with uniform finite spectra. For fixed quantum constants and large N there are three broad classes of FLHO: soft, medium, and hard corresponding respectively to cases where ratio of the of potential energy to kinetic energy in the Hamiltonian is very small, almost equal to one, or very large
The field oscillators responsible for infra-red and
ultraviolet divergences are soft and hard respectively. Medium oscillators approximate the QLHO. Their
low-lying states have nearly the same zero-point
energy and level spacing as the QLHO, and nearly obeying the Heisenberg uncertainty principle and the equipartition principle. The corresponding rotators are nearly polarized along the z-axis.
The soft and hard FLHO's have infinitesimal
0-point energy and grossly violate equipartition and the Heisenberg uncertainty principle. They do not resemble the QLHO at all. Their low-lying energy states correspond to rotators polaroizd along x-axis or y-axis respectively. Soft oscillators have
frozen momentum, because their maximum potential energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to produce one quantum of momentum. Hard oscillators have frozen position, because their maximum kinetic energy is too small to excite one quantum of position.
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Akten, Burcu Elif. "Generalized uncertainty relations /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.
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Prata, Guilherme Nery. "Novos funcionais para o modelo de Heisenberg anisotrópico." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-02072008-155051/.
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O modelo de Heisenberg destaca-se no estudo do magnetismo com origem em momentos magnéticos localizados. Semelhante ao bem conhecido modelo clássico de Ising, ele incorpora, no entanto, flutuações quânticas. Estamos interessados em sistemas antiferromagnéticos descritos pelo Hamiltoniano de Heisenberg com anisotropia de troca e que, eventualmente, possam apresentar magnetizações não-nulas. Neste trabalho, lidamos com sistemas não-homogêneos, apresentando impurezas e/ou sujeitos a condições de contorno abertas. Para tanto, utilizamos a Teoria do Funcional da Densidade, que proporciona uma metodologia de obtenção de resultados para um sistema não-homogêneo a partir dos resultados conhecidos do mesmo sistema quando homogêneo. Nosso trabalho resume-se a duas partes. Na primeira parte, trabalhamos inicialmente com um funcional, na aproximação ``local para o spin\'\'(LSA), advindo da Teoria de Ondas de Spin, válido para anisotropia de troca com simetria XXZ e magnetização do sistema nula. E na segunda, exploramos a possibilidade de construção de um funcional, na aproximação LSA, válido para anisotropia de troca mas com um adicional: válido para magnetizações não-nulas. Os resultados advindos dos funcionais são confrontados com resultados numericamente exatos obtidos de um programa em Fortran 90, que diagonaliza cadeias de spins na presença ou não de impurezas, para qualquer condição de contorno, descritas pelo modelo de Heisenberg com anisotropia de troca.The Heisenberg Model is generally recognized in the study of electromagnetism with origin in localized magnetic moments. Similar to the well known classical Ising model, it incorporates, however, quantum flutuations. We are interested in antiferromagnetic systems described by the Heisenberg Hamiltonian with exchange anisotropy and, eventually, non-null magnetizations. In this work, we deal with non-homogeneous systems with impurities. For this, we use Density Functional Theory and the Local Spin Aproximation (LSA), which provide a methodology for obtaining results of a non-homogeneous system from known results of the same but homogeneous system. Initially, we work with a functional provided by Spin Wave Theory on the LSA approximation, valid for anisotropies with XXZ simmetry and null magnetization. After that, we deal with the possibility of building a functional on LSA approximation valid also for exchange anisotropy but with an additional: applicable for non-null magnetizations.
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Schubert, Luke. "Spectral properties of the Laplacian on p-forms on the Heisenberg group /." Title page, contents and abstract only, 1997. http://web4.library.adelaide.edu.au/theses/09PH/09phs384.pdf.
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Brodlie, Alastair Robert. "Relationships between quantum and classical mechanics using the representation theory of the Heisenberg group." Thesis, University of Leeds, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.410635.
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Penteado, Poliana Heiffig. "Modelo de Heisenberg antiferromagnético com interações não-uniformes." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/76/76131/tde-28082008-115020/.
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Nesta dissertação, estudamos cadeias unidimensionais antiferromagnéticas de spins 1/2 modeladas pelo Hamiltoniano de Heisenberg na presença de inomogeneidades causadas principalmente pela introdução de ligações substitucionais (defeitos nas ligações) e por efeitos de borda. Interessados então em determinar a energia do estado fundamental de sistemas com quaisquer distribuições das ligações, utilizamos o formalismo da Teoria do Funcional da Densidade (DFT) desenvolvido para o modelo de Heisenberg. O formalismo da DFT permite a estimativa da energia do estado fundamental de sistemas não-homogêneos conhecendo-se o sistema homogêneo. Construímos funcionais na aproximação da ligação local (LBA), proposta recentemente em analogia à já conhecida LSA (aproximação local para o spin). A obtenção dos funcionais se baseou no estudo do modelo de uma cadeia de spins em que as ligações são alternadas, isto é, a interação de troca se alterna em valor de sítio para sítio. Isso originou um funcional não-local na interação de troca da cadeia. Apesar disso, continuamos utilizando a nomenclatura LBA. Todos os resultados fornecidos pelos funcionais são comparados a dados provenientes de diagonalização numérica exata.In this dissertation, we use the Heisenberg model to describe inhomogeneous antiferromagnetic spin 1/2 chains. The translational invariance is broken mainly due to the non-uniform distribution of bond interactions (defects) and the presence of boundaries. Interested in obtaining the ground-state energy of systems with any distribution of exchange couplings (Jij), we use the density-functional theory (DFT) formalism, developed for the Heisenberg model. The DFT formalism allows an estimate of the ground-state energy of inhomogeneous systems based on the homogeneous systems. We build functionals for the ground-state energy using a local bond approximation (LBA), recently proposed in analogy to the already known LSA (local spin approximation). To obtain the functionals we studied a model that describes an alternating chain, in which the exchange coupling alternates from site-to-site. This resulted in non-local functionals on the spin-spin exchange interaction. Nevertheless, we still call them LBA functionals. All the results from the functionals are compared with exact numerical data.
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Tashiro, Kenshiro. "Gromov-Hausdorff limits of compact Heisenberg manifolds with sub-Riemannian metrics." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263433.
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Hansson, Anders. "Spectral estimates for the magnetic Schrödinger operator and the Heisenberg Laplacian." Doctoral thesis, KTH, Matematik (Inst.), 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4578.
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I denna avhandling, som omfattar fyra forskningsartiklar, betraktas två operatorer inom den matematiska fysiken. De båda tidigare artiklarna innehåller resultat för Schrödingeroperatorn med Aharonov-Bohm-magnetfält. I artikel I beräknas spektrum och egenfunktioner till denna operator i R2 explicit i ett antal fall då en radialsymmetrisk skalärvärd potential eller ett konstant magnetfält läggs till. I flera av de studerade fallen kan den skarpa konstanten i Lieb-Thirrings olikhet beräknas för γ = 0 och γ ≥ 1. I artikel II bevisas semiklassiska uppskattningar för moment av egenvärdena i begränsade tvådimensionella områden. Vidare presenteras ett exempel då den generaliserade diamagnetiska olikheten, framlagd som en förmodan av Erdős, Loss och Vougalter, är falsk. Numeriska studier kompletterar dessa resultat. De båda senare artiklarna innehåller ett flertal spektrumuppskattningar för Heisenberg-Laplace-operatorn. I artikel III bevisas skarpa olikheter för spektret till Dirichletproblemet i (2n + 1)-dimensionella områden med ändligt mått. Låt λk och μk beteckna egenvärdena till Dirichlet- respektive Neumannproblemet i ett område med ändligt mått. N. D. Filonov har bevisat olikheten μk+1 < λk för den euklidiska Laplaceoperatorn. I artikel IV visas detta resultat för Heisenberg-Laplaceoperatorn i tredimensionella områden som uppfyller vissa geometriska villkor.In this thesis, which comprises four research papers, two operators in mathe- matical physics are considered. The former two papers contain results for the Schrödinger operator with an Aharonov-Bohm magnetic field. In Paper I we explicitly compute the spectrum and eigenfunctions of this operator in R2 in a number of cases where a radial scalar potential and/or a constant magnetic field are superimposed. In some of the studied cases we calculate the sharp constants in the Lieb-Thirring inequality for γ = 0 and γ ≥ 1. In Paper II we prove semi-classical estimates on moments of the eigenvalues in bounded two-dimensional domains. We moreover present an example where the generalised diamagnetic inequality, conjectured by Erdős, Loss and Vougalter, fails. Numerical studies complement these results. The latter two papers contain several spectral estimates for the Heisenberg Laplacian. In Paper III we obtain sharp inequalities for the spectrum of the Dirichlet problem in (2n + 1)-dimensional domains of finite measure. Let λk and μk denote the eigenvalues of the Dirichlet and Neumann problems, respectively, in a domain of finite measure. N. D. Filonov has proved that the inequality μk+1 < λk holds for the Euclidean Laplacian. In Paper IV we extend his result to the Heisenberg Laplacian in three-dimensional domains which fulfil certain geometric conditions.
QC 20100712
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Silva, Luiz Ben Hassanal Machado da [UNIFESP]. "A crise da objetividade, a epistemologia popperiana e o “programa de Heisenberg”." Universidade Federal de São Paulo (UNIFESP), 2015. http://repositorio.unifesp.br/handle/11600/39234.
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Nessa investigação nos concentraremos no período de consolidação da teoria quântica, sobretudo naquilo que toca o livro A Lógica da Pesquisa Científica, de 1934. O centro da investigação é à crítica de Popper ao pensamento indutivista e subjetivista de Heisenberg, que por meio de considerações da filosofia da linguagem e com o apoio de defensores da filosofia positivista, construiu com outros partidários da chamada Interpretação de Copenhague a interpretação hegemônica da teoria quântica. O dedutivismo realista de Popper , apresentado no livro Lógica da Pesquisa Científica, visa combater essa visão, através de uma defesa da objetividade e do realismo que escapou dos limites da Epistemologia e ganhou ares éticos. Popper defendeu a Interpretação Estatística, que é um ramo da teoria corpuscular. Demonstraremos como que a interpretação acerca do alcance da Epistemologia opõe esses pensadores. Para Heisenberg a objetividade devia ser deixada de lado, a partir da constatação empírica do Princípio de Incerteza. O método científico deve, segundo o físico alemão, limitar os conceitos da linguagem clássica e aplica-los nas descrições dos fenômenos quânticos segundo as limitações operacionais dos conceitos. Para Popper, a metodologia dispensa questões linguísticas e apreende o método científico como sendo baseado na testabilidade, o que impõe que a análise epistemológica seja feita somente após a teoria ter sido conjecturada. Investigaremos a partir do pensamento de Popper e veremos como sua defesa do falseacionismo impõe uma interpretação da teoria quântica diferente daquela preconizada por Heisenberg.
In this investigation we will focus on the period of consolidation of the quantum theory, specially, on what concerns the book Logic of Scientific Discovery, of 1934. The center of this investigation is the Popper‟s critics to the inductivism and subjectivism of Heisenberg thought that, through concepts of the philosophy of language and the support of positivist philosophy advocates, built with other supporters of Copenhagen Interpretation, the hegemonic interpretation of quantum theory. The realistic deductivism of Popper, submitted in the Logic of Scientific Discovery, aim to tackle this position, through a defense of objectivity and realism that pushed the boundaries of epistemology and acquired ethical air. Popper supported the statistical interpretation of quantum theory, a branch of corpuscular interpretation. We will show how the interpretation of the epistemological range opposes these thinkers. To Heisenberg the objectivity must be set apart from the empirical realization of the Principle of Uncertainty. The scientific method, according to the German physicist, must limit the concepts of classical language and apply them in the quantum phenomena descriptions according to the operational limitations of concepts. According to Popper, the methodology exempts linguistic questions and perceives the scientific method as grounded on testability, which imposes that the epistemological analysis has to be made only after the theory has been conjectured. We will investigate from the thought of Popper and we will see how his defense of falseacionism imposes an interpretation of the quantum theory different from those preconized by Heisenberg.
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Jarrett, Kieran. "Non-singular actions of countable groups." Thesis, University of Bath, 2018. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.761021.
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In this thesis we study actions of countable groups on measure spaces underthe assumption that the dynamics are non-singular, with particular reference topointwise ergodic theorems and their relationship to the critical dimensions ofthe action.
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Juhász, Junger Irén [Verfasser], Dieter [Akademischer Betreuer] Ihle, Dieter [Gutachter] Ihle, and Wolfgang [Gutachter] Nolting. "Green-function theory of anisotropic Heisenberg magnets with arbitrary spin / Irén Juhász Junger ; Gutachter: Dieter Ihle, Wolfgang Nolting ; Betreuer: Dieter Ihle." Leipzig : Universitätsbibliothek Leipzig, 2011. http://d-nb.info/1237894670/34.
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Goetze, Wolf Daniel. "Finite temperature dynamical structure factors of low dimensional strongly correlated systems." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:a7d1c49c-4d2b-45a8-854a-aad7f7e18f72.
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We determine the dynamical structure factors of two gapped correlated electron systems, namely the Ising model in a strong transverse field and the two-leg spin-1/2 Heisenberg ladder in the limit of strong rung coupling. We consider the low-temperature limit, employing a variety of analytical and numerical techniques. The coherent modes of single-particle excitations, which are delta functions at zero temperature, are shown to broaden asymmetrically in energy with increasing temperature. Firstly, we apply a low-temperature “resummation” inspired by the Dyson equation to a linked-cluster expansion of the two-leg Heisenberg ladder. We include matrix elements to second order in the interaction between states containing up to two particles. A low-frequency response similar to the “Villain mode” is also observed. Next, we apply a cumulant expansion technique to the transverse field Ising model. We resolve the issue of negative spectral weight caused by double pole in the leading self-energy diagram by including a resummation of terms obtained from the six-point function, demonstrating that the perturbation series in 2n-spin correlation functions can be extended to higher orders. The result generalises to higher dimensions and the analytic calculation is compared to a numerical Pade approximant. We outline the extension of this method to the strong coupling ladder. Finally, we compare the previous results to numerical data obtained by full diagonalisation of finite chains and numerical evaluation of the Pfaffian, a method specific to the transverse field Ising chain. The latter method is used for a phenomenological study of the asymmetric broadening as well as an evaluation of fitting functions for the broadened lineshapes.
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Childers, Kristen Snyder. "Generalizations of a Laplacian-Type Equation in the Heisenberg Group and a Class of Grushin-Type Spaces." Scholar Commons, 2011. http://scholarcommons.usf.edu/etd/3042.
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In [2], Beals, Gaveau and Greiner find the fundamental solution to a 2-Laplace-type equation in a class of sub-Riemannian spaces. This fundamental solution is based on the well-known fundamental solution to the p-Laplace equation in Grushin-type spaces [4] and the Heisenberg group [6]. In this thesis, we look to generalize the work in [2] for a p-Laplace-type equation. After discovering that the "natural" generalization fails, we find two generalizations whose solutions are based on the fundamental solution to the p-Laplace equation.
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Rekuc, Steven Joseph. "Eliminating Design Alternatives under Interval-Based Uncertainty." Thesis, Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7218.
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Typically, design is approached as a sequence of decisions in which designers select what they believe to be the best alternative in each decision. While this approach can be used to arrive at a final solution quickly, it is unlikely to result in the most-preferred solution. The reason for this is that all the decisions in the design process are coupled. To determine the most preferred alternative in the current decision, the designer would need to know the outcomes of all future decisions, information that is currently unavailable or indeterminate. Since the designer cannot select a single alternative because of this indeterminate (interval-based) uncertainty, a set-based design approach is introduced. The approach is motivated by the engineering practices at Toyota and is based on the structure of the Branch and Bound Algorithm. Instead of selecting a single design alternative that is perceived as being the most preferred at the time of the decision, the proposed set-based design approach eliminates dominated design alternatives: rather than selecting the best, eliminate the worst. Starting from a large initial design space, the approach sequentially reduces the set of non-dominated design alternatives until no further reduction is possible ??e remaining set cannot be rationally differentiated based on the available information. A single alternative is then selected from the remaining set of non-dominated designs.
In this thesis, the focus is on the elimination step of the set-based design method: A criterion for rational elimination under interval-based uncertainty is derived. To be efficient, the criterion takes into account shared uncertainty ??certainty shared between design alternatives. In taking this uncertainty into account, one is able to eliminate significantly more design alternatives, improving the efficiency of the set-based design approach. Additionally, the criterion uses a detailed reference design to allow more elimination of inferior design sets without evaluating each alternative in that set. The effectiveness of this elimination is demonstrated in two examples: a beam design and a gearbox design.
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Durham, Ian T. "Sir Arthur Eddington and the foundations of modern physics." Thesis, University of St Andrews, 2005. http://hdl.handle.net/10023/12933.
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In this dissertation I analyze Sir Arthur Eddington's statistical theory as developed in the first six chapters of his posthumously published Fundamental Theory. In particular I look at the mathematical structure, philosophical implications, and relevancy to modern physics. This analysis is the only one of Fundamental Theory that compares it to modern quantum field theory and is the most comprehensive look at his statistical theory in four decades. Several major insights have been made in this analysis including the fact that he was able to derive Pauli's Exclusion Principle in part from Heisenberg's Uncertainty Principle. In addition the most profound general conclusion of this research is that Fundamental Theory is, in fact, an early quantum field theory, something that has never before been suggested. Contrary to the majority of historical reports and some comments by his contemporaries, this analysis shows that Eddington's later work is neither mystical nor was it that far from mainstream when it was published. My research reveals numerous profoundly deep ideas that were ahead of their time when Fundamental Theory was developed, but that have significant applicability at present. As such this analysis presents several important questions to be considered by modern philosophers of science, physicists, mathematicians, and historians. In addition it sheds new light on Eddington as a scientist and mathematician, in part indicating that his marginalization has been largely unwarranted.
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Grechnyev, Oleksiy. "Theoretical Studies of Two-Dimensional Magnetism and Chemical Bonding." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4815.
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Bonneau, Ludovic. "Fission des noyaux lourds : étude microscopique des barrières de fission et du moment angulaire des fragments." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2003. http://tel.archives-ouvertes.fr/tel-00005374.
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Moura, Paulo Rogerio Garcez de. "CIÊNCIA E TÉCNICA EM HEIDEGGER E HEISENBERG." Universidade Federal de Santa Maria, 2009. http://repositorio.ufsm.br/handle/1/9082.
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Fundação de Amparo a Pesquisa no Estado do Rio Grande do SulThe classical physical science distinguishes itself as a previous project, consisting of the fundamental concepts of elements such as calculation, time, space, motion, matter, force and directed to capture all the nature phenomena supposedly unified. Quantum mechanics advances beyond these postulates, evidencing the inevitable interference of the subject in the search results , in which a reference to an ontological theory with material objects should be able to capture for regularities calculation, it becomes impossible, leaving the core concepts and field for the previous innovative project. As a result, the uncertainty principle that is expressed in a state of motion is identified only as to the statistical calculation or position, or the magnitude of the movement. After the development the existential concept of science that emphasizes the being-there as being-in-the-world to find certain beings as objects by the previous project of the scientific perspective, Heidegger subsequently comes to the conclusion that quantum physics incorporating the classical physics keeps unchangeable in terms of the previous science project of all: the nature disposes in advance a way of securing the meeting proposed by the existing human scientific achievement in theory terms . Science is only an access way to nature in its inexhaustible plenitude, so that it makes it unavoidable and unattainable with the scientificity resources. The com-position is the essence of the technique using scientific results and, by its vortex, enabling it to the final co-existing human. It remains to the being-there the mercy of a thought as to question the destitute condition of his own danger in forgetting that the cooption may be victim of their own decision.
A física clássica distingue-se como ciência por um projeto prévio, composto pelos conceitos fundamentais de elementos como cálculo, tempo, espaço, movimento, matéria, força e direcionado a captar todos os fenômenos da natureza supostamente unificada. A mecânica quântica avança além desses postulados, evidenciando a inevitável interferência do sujeito nos resultados de sua pesquisa, em que a referência a uma teoria ontológica com objetos materiais, devendo ser captáveis para fins de cálculo de regularidades, tornase impossível, restando os conceitos de núcleo e campo para o projeto prévio inovador. Em decorrência, o princípio de incerteza se expressa em que um estado de movimento se identifica somente quanto à calculabilidade estatística ou da posição, ou da grandeza do movimento. Após a elaboração do conceito existencial de ciência, que ressalta o seraí como ser-no-mundo a encontrar entes determinados como objetos pelo projeto prévio da perspectiva científica, Heidegger posteriormente chega à conclusão de que a física quântica incorporando a física clássica permanece imutável no que concerne ao projeto prévio da ciência de sempre: a natureza se dispõe de antemão a um encontro ao modo de asseguramento proposto pelo existente humano numa realização científica em termos de teoria. A ciência permanece apenas como um dos modos de acesso à natureza em sua plenitude inesgotável, o que faz com que ela seja incontornável e inacessível com os recursos da cientificidade. A com-posição é a essência da técnica utilizando resultados científicos e, pela sua voragem, habilitando-se para a cooptação definitiva do existente humano. Resta ao ser-aí a piedade de um pensamento indigente enquanto questionar a sua própria condição de perigo no esquecimento da cooptação de que pode ser vítima por própria decisão.
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Olovsson, Weine. "Influence of Global Composition and Local Environment on the Spectroscopic and Magnetic Properties of Metallic Alloys." Doctoral thesis, Uppsala University, Department of Physics, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5823.
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Theoretical investigations of spectroscopic and magnetic properties of metallic systems in the bulk, as well as in nanostructured materials, have been performed within the density functional theory. The major part of the present work studies the differences between binding energies of electrons tightly bound to the atoms, the so-called core electrons (in contrast with the valence electrons), that is, core-level binding energy shift (CLS).
By comparison between corresponding elemental core-levels for atoms situated in different chemical environments we obtain fundamental understanding of bonding properties of materials. The method of choice was the complete screening picture, which includes initial and final state effects on the same footing. The usefulness of CLS stems from that it is sensitive to differences in the chemical environment of an atom, which can be affected on one hand by the global composition of e.g. disordered materials, surfaces and interfaces, and on the other hand by the very local environment around an atom. Here CLSs have been obtained for both components in the fcc random alloys AgPd, CuPd, CuNi, CuPt, CuAu, PdAu, NiPd and NiPt. Moreover the model was extended to the Auger kinetic energy shift for the LMM Auger transition in AgPd alloys. Studies were also applied to the near surface and interface regions of PdMn nano structures on Pd(100), thin CuPd and AgPd films on inert Ru(0001), and at interfaces. The disorder broadening on CLS due to local environment effects was calculated in selected alloys.
A part of the thesis concern investigations related to the magnetic ordering in Invar alloys, including the influence of local environment effects. A study was made for the dependence of effective exchange parameter on the electron concentration, volume and local chemical composition.
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Allalen, Mohammed. "Magnetic properties and proton spin-lattice relaxation in molecular clusters." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=979984777.
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Calisti, Matteo. "Differential calculus in metric measure spaces." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21781/.
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L'obbiettivo di questa tesi è la definizione del calcolo differenziale e dell'operatore di Laplace in spazi metrici di misura. Nel primo capitolo vengono introdotte le definizioni e proprietà principali degli spazi metrici di misura mentre nel secondo quelle riguardanti le funzioni lipschitziane e la derivata metrica di curve assolutamente continue. Nel terzo capitolo quindi viene definito il concetto di p-supergradiente debole e di conseguenza la classe di Sobolev S^p. Nel quarto capitolo viene poi studiata la generalizzazione del concetto di differenziale di f applicato al gradiente di g che da luogo a due funzioni che in generale risultano diverse, ma se coincidono lo spazio verrà detto q-infinitesimamente strettamente convesso.
Vengono quindi dimostrate alcune regole della catena per per queste due funzioni attraverso la dualità fra lo spazio S^p e un opportuno spazio di misure dette q-piani test. In particolare mediante l'introduzione del funzionale energia di Cheeger e il suo flusso-gradiente sarà possibile associare un piano di trasporto al gradiente di una funzione in S^p. Nel quinto capitolo viene definito il p-laplaciano e le regole di calcolo provate precedentemente saranno usate per provare quelle per il laplaciano. Verranno poi definiti gli spazi infitesimamente di Hilbert: in questo caso il laplaciano assume un solo valore e risulta linearmente dipendente da g e si dimostra un'identificazione tra differenziali e gradienti. Nell'ultima parte del quinto capitolo infine viene mostrata un'applicazione del calcolo differenziale in spazi metrici di misura al gruppo di Heisenberg, considerandolo uno spazio metrico di misura munito della metrica di Korany e la misura di Lebesgue. Nella prima parte si mostra che il laplaciano metrico coincide con quello subriemanniano. Viene poi considerata nella seconda parte la sottovarietà {x=0} e si dimostra come il laplaciano metrico sia diverso da quello differenziale.
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Jego, Charles. "Theories des champs conformes non rationnelles et applications a la theorie des cordes." Phd thesis, Ecole Polytechnique X, 2007. http://pastel.archives-ouvertes.fr/pastel-00002591.
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Cette these est dediee a l'etude de quelques theories conformes non rationnelles, qui apparaissent dans le cadre de la theorie des cordes. Contrairement aux theories conformes rationnelles, qui ont beneficie de tres nombreuses etudes dans les toutes dernieres decennies, les theories non rationnelles ne sont pas encore bien comprises. Une meilleure comprehension est pourtant necessaire pour mieux apprehender la theorie des cordes dans des fonds courbes non compacts, et pour pouvoir a terme s'attaquer a des problemes cosmologiques. Dans la mesure ou la these a frequemment recours a des notions et a des resultats de la theorie des groupes de Lie et de la theorie conforme des champs, des introductions detaillees a ces domaines sont presentees a l'attention des lecteurs qui ne sont pas familiarise avec eux. La these presente ensuite le travail qui a ete realise au cours du doctorat. Ce travail s'est attaque a des espaces presentant pour symetrie l'algebre de Heisenberg, a une extension de la formule de Verlinde pour des theories conformes non rationnelles (comme H_3^+), et aux cordes ouvertes rigides contraintes sur des orbites co-adjointes d'algebres de Lie.
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Petit, Camille. "Autour de l'analyse géométrique. 1) Comportement au bord des fonctions harmoniques 2) Rectifiabilité dans le groupe de Heisenberg." Phd thesis, Université de Grenoble, 2012. http://tel.archives-ouvertes.fr/tel-00744491.
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Dans cette thèse, nous nous intéressons à deux thèmes d'analyse géométrique. Le premier concerne le comportement asymptotique des fonctions harmoniques en relation avec la géométrie, sur des graphes et des variétés. Nous étudions des critères de convergence au bord des fonctions harmoniques, comme celui de la bornitude non-tangentielle, de la finitude de l'énergie ou encore de la densité de l'énergie. Nous nous plaçons pour cela dans différents cadres comme les graphes hyperboliques au sens de Gromov, les variétés hyperboliques au sens de Gromov, les graphes de Diestel-Leader ou encore dans un cadre abstrait pour obtenir des résultats pour les points du bord minimal de Martin. Les méthodes probabilistes utilisées exploitent le lien entre les fonctions harmoniques et les martingales. Le deuxième thème abordé dans cette thèse concerne l'étude des propriétés des ensembles rectifiables de dimension 1 dans le groupe de Heisenberg, en relation avec des opérateurs d'intégrales singulières. Nous étendons à ce contexte sous-riemannien une partie des résultats de la théorie des ensembles uniformément rectifiables de David et Semmes. Nous obtenons notamment un théorème géométrique du voyageur de commerce qui fournit une condition pour qu'un ensemble Ahlfors-régulier du premier groupe de Heisenberg soit contenu dans une courbe Ahlfors-régulière.
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Jego, Charles. "Théories des champs conformes non rationnelles et applications à la théorie des cordes." Palaiseau, Ecole polytechnique, 2007. http://www.theses.fr/2007EPXX0012.
Full textAbstract:
Cette these est dediee a l'etude de quelques theories conformes non rationnelles, qui apparaissent dans le cadre de la theorie des cordes. Contrairement aux theories conformes rationnelles, qui ont beneficie de tres nombreuses etudes dans les toutes dernieres decennies, les theories non rationnelles ne sont pas encore bien comprises. Une meilleure comprehension est pourtant necessaire pour mieux apprehender la theorie des cordes dans des fonds courbes non compacts, et pour pouvoir a terme s'attaquer a des problemes cosmologiques. Dans la mesure ou la these a frequemment recours a des notions et a des resultats de la theorie des groupes de Lie et de la theorie conforme des champs, des introductions detaillees a ces domaines sont presentees a l'attention des lecteurs qui ne sont pas familiarise avec eux. La these presente ensuite le travail qui a ete realise au cours du doctorat. Ce travail s'est attaque a des espaces presentant pour symetrie l'algebre de Heisenberg, a une extension de la formule de Verlinde pour des theories conformes non rationnelles (comme H_3^+), et aux cordes ouvertes rigides contraintes sur des orbites co-adjointes d'algebres de Lie.
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Pesce, Hubert. "Problèmes d'isospectralité pour les nilvariétés." Grenoble 1, 1991. http://www.theses.fr/1991GRE10170.
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Le laplacien d'une variete riemannienne compacte a un spectre discret qui s'appelle le spectre de la variete. Un probleme classique est de savoir si deux varietes isospectrales sont isometriques. Depuis le celebre contre-exemple de milnor, on sait que la reponse a ce probleme est negative. Dans la premiere partie, on donne une borne explicite du nombre de tores plats isospectraux a un tore donne et non deux a deux isometriques, borne dependant de la geometrie du tore donne. On utilise des resultats sur les formes quadratiques. En 1984, c. Gordon et e. Wilson ont construit les premiers exemples de deformations isospectrales. Les varietes qu'ils considerent sont des nilvarietes. Le but des deux dernieres parties est de montrer que toutes les deformations isospectrales des nilvarietes de rang deux sont celles construites par c. Gordon et e. Wilson. Dans la deuxieme partie, on demontre le resultat voulu dans le cas ou la nilvariete est non singuliere, puis on demontre qu'il n'y a qu'un nombre fini de classes d'isometrie de varietes de heisenberg isospectrales. Dans la troisieme partie, on calcule le spectre d'une nilvariete de rang deux en utilisant la theorie de kirillov et on caracterise les deformations isospectrales des nilvarietes de rang deux
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Lebed, Victoria. "Objets tressés : une étude unificatrice de structures algébriques et une catégorification des tresses virtuelles." Phd thesis, Université Paris-Diderot - Paris VII, 2012. http://tel.archives-ouvertes.fr/tel-00775857.
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Dans cette thèse on développe une théorie générale des objets tressés et on l'applique à une étude de structures algébriques et topologiques. La partie I contient une théorie homologique des espaces vectoriels tressés et modules tressés, basée sur le coproduit de battage quantique. La construction d'un tressage structurel qui caractérise diverses structures - auto-distributives (AD), associatives, de Leibniz - permet de généraliser et unifier des homologies familières. Les hyper-bords de Loday, ainsi que certaines opérations homologiques, apparaissent naturellement dans cette interprétation. On présente ensuite des concepts de système tressé et module multi-tressé. Appliquée aux bigèbres, bimodules, produits croisés et (bi)modules de Hopf et de Yetter-Drinfel'd, cette théorie donne leurs interprétations tressées, homologies et actions adjointes. La no- tion de produits tensoriels multi-tressés d'algèbres donne un cadre unificateur pour les doubles de Heisenberg et Drinfel'd, ainsi que les algèbres X de Cibils-Rosso et Y et Z de Panaite. La partie III est orientée vers la topologie. On propose une catégorification des groupes de tresses virtuelles en termes d'objets tressés dans une catégorie symétrique (CS). Cette approche de double tressage donne une source de représentations de V Bn et un traitement catégorique des racks virtuels de Manturov et de la représentation de Burau tordue. On définit ensuite des structures AD dans une CS arbitraire et on les munit d'un tressage. Les techniques tressées de la partie I amènent alors à une théorie homologique des structures AD catégoriques. Les algèbres associatives, de Leibniz et de Hopf rentrent dans ce cadre catégorique.
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Kozhevnikov, Artem. "Propriétés métriques des ensembles de niveau des applications différentiables sur les groupes de Carnot." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112073/document.
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Nous étudions les propriétés métriques locales des ensembles de niveau des applicationshorizontalement différentiables entre des groupes de Carnot, c'est-à-dire différentiable par rapport à la structure sous-riemannienne intrinsèque.Nous considérons des applications dont la différentielle horizontale est surjective,et notre étude peut être vue comme une généralisation du théorème des fonctions implicites pour les groupes de Carnot.Tout d'abord, nous présentons deux notions de tangence dans les groupes de Carnot:la première basée sur la condition de platitude au sens de Reifenberg et la deuxième issue de l'analyse convexe classique.Nous montrons que dans les deux cas, l'espace tangent à un ensemble de niveau coïncide avec le noyau de la différentielle horizontale.Nous montrons que cette condition de tangence caractérise en fait les ensembles de niveaudits ‘co-abéliens', c'est-à-dire ceux pour lesquels l'espace d'arrivée est abélien, et qu'une telle caractérisation n'est pas vraie en général.Ce résultat sur les espaces tangents a plusieurs conséquences remarquables.La plus importante est que la dimension de Hausdorff des ensembles de niveau est celle à laquelle l'on s'attend.Nous montrons également la connectivité locale des ensembles de niveau, et le fait que les ensembles de niveau de dimension 1 sont topologiquement des arcs simples.Pour les ensembles de niveau de dimension 1 nous trouvons une formule de l'aire qui permet d'exprimer la mesure de Hausdorff en termes d'intégrales de Stieltjes généralisées.Ensuite, nous menons une étude approfondie du cas particulier des ensembles de niveau dans les groupes d'Heisenberg.Nous montrons que les ensembles de niveau sont topologiquement équivalents à leurs espaces tangents.Il s'avère que la mesure de Hausdorff des ensembles de niveau de codimension élevée est souvent irrégulière, étant, par exemple, localement nulle ou infinie.Nous présentons une condition simple de régularité supplémentaire pour une application pour assurer la régularité au sens d'Ahlfors des ses ensembles de niveau.Parmi d'autres résultats, nous obtenons une nouvelle caractérisation généraledes graphes Lipschitziens associés à une décomposition en produit semi-direct d'un groupe de Carnot.Nous traitons, en particulier, le cas des groupes de Carnot dont le nombre de stratesest plus grand que $2$.Cette caractérisation nous permet de déduire une nouvelle caractérisation des ensemblesde niveau co-abéliens qui admettent une représentation en tant que grapheMetric properties of level sets of differentiable maps on Carnot groupsAbstract.We investigate the local metric properties of level sets of mappings defined between Carnot groups that are horizontally differentiable, i.e.with respect to the intrinsic sub-Riemannian structure. We focus on level sets of mapping having a surjective differential,thus, our study can be seen as an extension of implicit function theorem for Carnot groups.First, we present two notions of tangency in Carnot groups: one based on Reifenberg's flatness condition and another coming from classical convex analysis.We show that for both notions, the tangents to level sets coincide with the kernels of horizontal differentials.Furthermore, we show that this kind of tangency characterizes the level sets called ``co-abelian'', i.e.for which the target space is abelian andthat such a characterization may fail in general.This tangency result has several remarkable consequences.The most important one is that the Hausdorff dimension of the level sets is the expected one. We also show the local connectivity of level sets and, the fact that level sets of dimension one are topologically simple arcs.Again for dimension one level set, we find an area formula that enables us to compute the Hausdorff measurein terms of generalized Stieltjes integrals.Next, we study deeply a particular case of level sets in Heisenberg groups. We show that the level sets in this case are topologically equivalent to their tangents.It turns out that the Hausdorff measure of high-codimensional level sets behaves wildly, for instance, it may be zero or infinite.We provide a simple sufficient extra regularity condition on mappings that insures Ahlfors regularity of level sets.Among other results, we obtain a new general characterization of Lipschitz graphs associated witha semi-direct splitting of a Carnot group of arbitrary step.We use this characterization to derive a new characterization of co-ablian level sets that can be represented as graphs
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Sharify, Romyar T. "Twisted Heisenberg representations and local conductors /." 1999. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:9934118.
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Jung, Peter [Verfasser]. "Weyl-Heisenberg representations in communication theory / vorgelegt von Peter Jung." 2007. http://d-nb.info/985287659/34.
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Juhász, Junger Irén. "Green-function theory of anisotropic Heisenberg magnets with arbitrary spin." Doctoral thesis, 2010. https://ul.qucosa.de/id/qucosa%3A11228.
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In this thesis, anisotropic Heisenberg magnets with arbitrary spin are investigated within the second-order Green-function theory. Three models are considered.
First, the second-order Green-fuction theory for one-dimensional and two-dimensional Heisenberg ferromagnets with arbitrary spin S in a
magnetic field is developed. For the determination of the introduced vertex parameters sum rules, higher-derivative sum rules, and regularity conditions are derived, and the equality of the isothermal and the longitudinal uniform static Kubo susceptibilities is required. Thermodynamic quantities, such as the specific heat, magnetic susceptibility, transverse and longitudinal correlation lengths are calculated. Empirical formulas describing the dependence of the position and height of the susceptibility maximum on the magnetic field are given. An anomal behavior of the longitudinal correlation length is observed. The appearance of two maxima in the temperature dependence of the specific heat is discussed.
Further, as an example of a system with an anisotropy in the spin space, the S=1 ferromagnetic chain with easy-axis single-ion anisotropy is studied. Justified by the up-down symmetry of the model with respect to $S_i^z -> -S_i^z$, $\\langle S_i^z \\rangle=0$ is set. Two different ways of the determination of the introduced vertex parameters are presented. The transverse nearest-neighbor correlation function, spin-wave spectrum and longitudinal correlation length are analyzed. The effects of the single-ion anisotropy on the transverse and longitudinal uniform static
susceptibilities as well as on the appearance of two maxima in the temperature dependence of the specific heat are examined.
Finally, as examples of spatial anisotropic spin systems,layered Heisenberg
ferromagnets and antiferromagnets with arbitrary spin are studied within the rotation-invariant Green-function theory. The long-range order is described by the condensation term, which is determined from the requirement that in the ordered state the static susceptibility has to diverge at the ordering wave vector. For determination of the introduced vertex parameters, the sum rule and the isotropy condition are used and also assumptions regarding the temperature dependence of some parameters are made. The main focus is put on the calculation of the specific heat, the Curie temperature, and the Néel temperature in dependence on the interlayer coupling and the spin-quantum number. Empirical formulas describing the dependence of the transition temperatures on the ratio of interlayer and intralayer couplings are given.
For all three models, the results of the Green-function theory are compared to available results of exact approaches (Quantum Monte Carlo, exact diagonalization, Bethe-ansatz method) and to available experimental data.
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"Numerical studies of thermal properties of the two-dimensional Heisenberg model." 2001. http://library.cuhk.edu.hk/record=b5890686.
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Lee Kwok San = 二維海森堡模型的熱力學性質之數値硏究 / 李國姗.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.
Includes bibliographical references (leaves 106-108).
Text in English; abstracts in English and Chinese.
Lee Kwok San = Er wei hai sen bao mo xing de re li xue xing zhi zhi shu zhi yan jiu / Li Guoshan.
Abstract --- p.i
Acknowledgement --- p.iii
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- History of magnetism --- p.1
Chapter 1.2 --- History of Heisenberg model --- p.2
Chapter 1.3 --- Heisenberg model and high-Tc superconductors --- p.6
Chapter 1.4 --- Organization of thesis --- p.8
Chapter 2 --- Methodology --- p.10
Chapter 2.1 --- Introduction --- p.10
Chapter 2.2 --- Exact diagonalization --- p.11
Chapter 2.2.1 --- Coding with only total Sz conservation --- p.11
Chapter 2.2.2 --- Coding by using translational symmetry --- p.12
Chapter 2.2.3 --- Coding with H acting on spin configuration --- p.17
Chapter 2.2.4 --- Coding on finding eigenvalues and eigenvectors --- p.20
Chapter 2.3 --- Coding on calculating dynamic properties --- p.20
Chapter 2.3.1 --- Coding on calculating thermal properties --- p.20
Chapter 2.3.2 --- Coding on calculating other thermal property --- p.21
Chapter 3 --- Finite temperature calculations on unfrustrated spin systems --- p.30
Chapter 3.1 --- Introduction --- p.30
Chapter 3.2 --- Finite temperature calculations --- p.33
Chapter 3.2.1 --- Energy spectrum E(k) --- p.33
Chapter 3.2.2 --- Internal energy (E) --- p.39
Chapter 3.2.3 --- Heat capacity Cv --- p.42
Chapter 3.2.4 --- Uniform susceptibility x --- p.45
Chapter 3.2.5 --- Staggered magnetization mz+ --- p.47
Chapter 3.3 --- Linear Spin Wave Theory --- p.48
Chapter 3.3.1 --- Linear Spin Wave Theory at zero temperature --- p.48
Chapter 3.3.2 --- Linear Spin Wave Theory at finite temperature --- p.54
Chapter 3.4 --- Phase Transition --- p.57
Chapter 4 --- Finite temperature calculations on frustrated systems --- p.62
Chapter 4.1 --- Introduction --- p.62
Chapter 4.2 --- Finite temperature calculations --- p.65
Chapter 4.2.1 --- Energy spectrum E(k) --- p.65
Chapter 4.2.2 --- Internal energy (E) --- p.68
Chapter 4.2.3 --- Heat capacity Cv --- p.69
Chapter 4.2.4 --- Uniform susceptibility x --- p.71
Chapter 4.2.5 --- "Fourier transform of susceptibility S(qx,qy)" --- p.72
Chapter 4.3 --- Linear Spin Wave Theory --- p.73
Chapter 5 --- Finite Size Scaling --- p.78
Chapter 5.1 --- Introduction --- p.78
Chapter 5.2 --- Infinite unfrustrated system --- p.79
Chapter 5.2.1 --- Ground state energy E0 --- p.79
Chapter 5.2.2 --- Internal Energy (E) --- p.80
Chapter 5.2.3 --- Staggered magnetization mz+ --- p.81
Chapter 5.3 --- Infinite frustrated system --- p.83
Chapter 5.3.1 --- Ground state energy E0 --- p.84
Chapter 6 --- Comparisons between unfrustrated system and frustrated system --- p.87
Chapter 6.1 --- Energy spectrum E(k) --- p.88
Chapter 6.2 --- Internal energy (E) --- p.91
Chapter 6.3 --- Heat capacity Cv --- p.92
Chapter 6.4 --- Uniform susceptibility x --- p.93
Chapter 7 --- Spin Lattice Relaxation l/T1 --- p.94
Chapter 7.1 --- Introduction --- p.94
Chapter 7.2 --- Spin temperature --- p.95
Chapter 7.3 --- Experimental setup and its principle --- p.97
Chapter 7.4 --- Numerical calculations --- p.102
Chapter 8 --- Conclusion --- p.104
Bibliography --- p.106
Chapter A --- Method of moments --- p.109
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Flores, Manuel. "L²-theory for [d-bar-b] on some rigid generalizations of the Heisenberg group." 1998. http://catalog.hathitrust.org/api/volumes/oclc/40350125.html.
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Thesis (Ph. D.)--University of Wisconsin--Madison, 1998.Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 72-75).
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Samanta, Amit. "Joint Eigenfunctions On The Heisenberg Group And Support Theorems On Rn." Thesis, 2012. http://etd.iisc.ernet.in/handle/2005/2289.
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This work is concerned with two different problems in harmonic analysis, one on the Heisenberg group and other on Rn, as described in the following two paragraphs respectively.
Let Hn be the (2n + 1)-dimensional Heisenberg group, and let K be a compact subgroup of U(n), such that (K, Hn) is a Gelfand pair. Also assume that the K-action on Cn is polar. We prove a Hecke-Bochner identity associated to the Gelfand pair (K, Hn). For the special case K = U(n), this was proved by Geller, giving a formula for the Weyl transform of a function f of the type f = Pg, where g is a radial function, and P a bigraded solid U(n)-harmonic polynomial. Using our general Hecke-Bochner identity we also characterize (under some conditions) joint eigenfunctions of all differential operators on Hn that are invariant under the action of K and the left action of Hn .
We consider convolution equations of the type f * T = g, where f, g ε Lp(Rn) and T is a compactly supported distribution. Under natural assumptions on the zero set of the Fourier transform of T , we show that f is compactly supported, provided g is.
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Chen, Bryce, and 陳怡中. "Subdivergence theorem on Heisenberg group." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/d76t36.
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碩士國立中央大學
數學系
106
In this thesis, we use the Stokes’ theorem to establish a subdivergence theorem for the Heisenberg groups which is analogue of the divergence theorem on Riemannian manifolds.
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Guerra, Rita Catarina Correia. "Generalizations of the Fourier transform and their applications." Doctoral thesis, 2019. http://hdl.handle.net/10773/29813.
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In this thesis, we consider a new generalization of the Fourier transform,
depending on four complex parameters and all the powers of the Fourier
transform. This new transform is studied in some Lebesgue spaces. In fact,
taking into account the values of the parameters of the operator, we can
have very different kernels and so, the corresponding operator is studied in
different Lebesgue spaces, accordingly with its kernel.
We begin with the characterization of each operator by its characteristic polynomial. This characterization serves as a basis for the study
of the forthcoming properties. Following this, we present, for each case,
the spectrum of the corresponding operator, necessary and sufficient
conditions for which the operator is invertible, Parseval-type identities and
conditions for which the operator is unitary and an involution of order n.
After this, we contruct new convolutions associated with those operators
and obtain the corresponding factorization identities and some norm
inequalities. By using these new operators and convolutions, we construct
new integral equations and study their solvability. In this sense, we have
equations generated by the studied operators and also a class of equations
of convolution-type depending on multi-dimensional Hermite functions.
Furthermore, we study the solvability of classical integral equations, using
the new operators and convolutions, namely a class of Wiener-Hopf plus
Hankel equations, whose solution is written in terms of a Fourier-type series.
For one case of this generalization of the Fourier transform, that
only depends on the cosine and sine Fourier transforms, we obtain PaleyWiener and Wiener’s Tauberian results, using the associated convolution
and a new translation induced by that convolution. Heisenberg uncertainty
principles for the one-dimensional case and for the multi-dimensional case
are obtained for a particular case of the introduced operator.
At the end, as an application outside of mathematics, we obtain a
new result in signal processing, more properly, in a filtering processing, by
applying one of our new convolutions.Nesta tese, consideramos uma nova generalização da transformação de Fourier, dependente de quatro parâmetros complexos e de todas as potências da transformação de Fourier. Esta nova transformação é estudada em alguns espaços de Lebesgue. De facto, tendo em conta os valores dos parâmetros, podemos ter núcleos muito diferentes e assim, o correspondente operador é estudado em diferentes espaços de Lebesgue, de acordo com o seu núcleo. Começamos com a caracterização de cada operador pelo seu polinómio característico. Esta caracterização serve de base para o estudo das propriedades seguintes. Seguindo isto, apresentamos, para cada caso, o espetro do correspondente operador, condições necessárias e suficientes para as quais o operador é invertível, identidades do tipo de Parseval e condições para as quais o operador é unitário e uma involução de ordem n. Depois disto, construímos novas convoluções associadas àqueles operadores e obtemos as correspondentes identidades de factorização e algumas desigualdades da norma. Usando estes novos operadores e convoluções, construímos novas equações integrais e estudamos a sua solvabilidade. Neste sentido, temos equações geradas pelos operadores estudados e também uma classe de equações do tipo de convolução dependendo de funções de Hermite multidimensionais. Além disso, estudamos a solvabilidade de equações integrais clássicas, usando os novos operadores e convoluções, nomeadamente uma classe de equações de Wiener-Hopf mais Hankel, cuja solução é escrita em termos de uma série do tipo de Fourier. Para um caso desta generalização da transformação de Fourier, que depende apenas das transformações de Fourier do cosseno e do seno, obtemos resultados de Paley-Wiener e resultados Tauberianos de Wiener, usando a convolução associada e uma nova translação induzida por essa convolução. Princípios de incerteza de Heisenberg para os casos unidimensional e multidimensional são obtidos para um caso particular do operador introduzido. No final, como uma aplicação fora da matemática, obtemos um novo resultado em processamento de sinal, mais propriamente, num processo de filtragem, por aplicação de uma das nossas novas convoluções.
Programa Doutoral em Matemática Aplicada
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Lai, Sin-Hua, and 賴馨華. "Perelman's Entropy Formula on Pseudohermitian Manifolds and Fundamental Theorem on Heisenberg Groups." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/86327994138869805427.
Full textAbstract:
博士國立中央大學
數學系
101
In this thesis, we study Perelman's W-Entropy formula for the CR heat equation associated with the Witten Laplacian on pseudohermitian manifolds via the Bakry-Emery Ricci curvature. In addition we establish the fundamental theorem for Legendrian submanifolds in Heisenberg groups. In Chapter 2, we derive the subgradient estimate of the CR heat equation associated with the Witten Laplacian on a closed pseudohermitian (2n+1)-manifold. With its application, we obtain Perelman-type entropy formula for thse CR heat equation and the CR heat equation associated with the Witten Laplacian. In Chapter 3, we obtain the representation of PSH(n) which is the group of pseudohermitian transformations on n-dimensional Heisenberg groups. Also we discuss how the matrix Lie group PSH(n) interpret as the set of "frames" on the homogeneous space PSH(n)/U(n). Then for the (left-invariant) Maurer-Cartan form, we immediately get the moving frame formula. In Chapter 4, we use Élie Cartan's method of moving frames, the theory of Lie groups to obtain the fundamental theorem for the Legendrian submanifolds in Hesenberg groups. Let Σ be a n-dimensional oriented surface and f:Σ-->H^n be an embedding as a Legendrian submanifold in H^n. For every totally real point p in Σ, we compute the Darboux derivative of the lifting of f to get the integrability conditions for Σ. Then we show that for any Riemannian manifold which satisfies the integrability conditions can be locally embedded into H^n as a Legendrian submanifold.
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(6943460), Roozbeh Gharakhloo. "Asymptotic Analysis of Structured Determinants via the Riemann-Hilbert Approach." Thesis, 2020.
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In this work we use and develop Riemann-Hilbert techniques to study the asymptotic behavior of structured determinants. In chapter one we will review the main underlying
definitions and ideas which will be extensively used throughout the thesis. Chapter two is devoted to the asymptotic analysis of Hankel determinants with Laguerre-type and Jacobi-type potentials with Fisher-Hartwig singularities. In chapter three we will propose a Riemann-Hilbert problem for Toeplitz+Hankel determinants. We will then analyze this Riemann-Hilbert problem for a certain family of Toeplitz and Hankel symbols. In Chapter four we will study the asymptotics of a certain bordered-Toeplitz determinant which is related to the next-to-diagonal correlations of the anisotropic Ising model. The analysis is based upon relating the bordered-Toeplitz determinant to the solution of the Riemann-Hilbert problem associated to pure Toeplitz determinants. Finally in chapter ve we will study the emptiness formation probability in the XXZ-spin 1/2 Heisenberg chain, or equivalently, the asymptotic analysis of the associated Fredholm determinant.
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Moosavi, Askari Reza. "Experimental and numerical study of a magnetic realization of a Bose-Einstein Condensate in a purely organic spin-1/2 quantum magnet (NIT2Py)." Thèse, 2016. http://hdl.handle.net/1866/20605.
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Bagchi, Sayan. "Weighted Norm Inequalities for Weyl Multipliers and Hermite Pseudo-Multipliers." Thesis, 2015. http://etd.iisc.ernet.in/2005/3641.
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In this thesis we deal with two problems in harmonic analysis. In the first problem we discuss weighted norm inequalities for Weyl multipliers satisfying Mauceri’s condition. As an application, we prove certain multiplier theorems on the Heisenberg group and also show in the context of a theorem of Weis on operator valued Fourier multipliers that the R-boundedness of the derivative of the multiplier is not necessary for the boundedness of the multiplier transform. In the second problem we deal with a variation of a theorem of Mauceri concerning the Lp bound-edness of operators Mwhich are known to be bounded on L2 .We obtain sufficient conditions on the kernel of the operaor Mso that it satisfies weighted Lp estimates. As an application we prove Lp boundedness of Hermite pseudo-multipliers.
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ČECH, František. "Princip komplementarity ve fyzice a jeho role při přípravě odborníků v oblasti ochrany obyvatelstva." Master's thesis, 2018. http://www.nusl.cz/ntk/nusl-386607.
Full textAbstract:
This diploma thesis on the application of logical, empirical and statistical methods defined the role of the complementarity principle in the preparation of experts in the field of the protection of population in the framework of a quantitative research. The complementarity principle is characterized in the thesis in general (working with two expressions, both of them are necessary to explain the nature of the problem but cannot be used simultaneously, e.g. expressions "analysis" and "synthesis"). The diploma thesis then defined the physical aspect of the complementarity principle the wave-corpuscular dualism, the position and the momentum, the energy and the time. The comparison of the basics of the protection of population with the structure of the physical aspect of the complementarity principle followed. The performed comparison was adjusted to the needs and possibilities of future experts in the field of the protection of population on the basis of the theory of the curriculum process. The steps are clear from the set of objectives which were fulfilled gradually in the thesis: 1) To systematically describe the general form of the complementarity principle and its physical application from the point of view of the theory of the curriculum process. 2) To create a structure of the system of emergencies from the point of view of a scientific field of the protection of population and to focus on its educational aspect for the preparation of experts. 3) To perform the comparison of the physical aspect and emergencies with the general form of the complementarity principle. To transfer the findings, a theory of curriculum process was used. The link between a more generally approached complementarity principle and the protection of population was explained in the framework of a conceptual curriculum. The theory connecting these two different fields is the more generally approached complementarity principle and especially Bohr's complementarity principle linking not only the wave-corpuscular dualism but also Heisenberg's uncertainty principle. The physical aspect of emergencies was adjusted to the possibilities and needs of students (the intended curriculum) and written down in an educational text which was provided to students (the project curriculum). The practicality of the educational test was verified by an educational test the results of which were statistically processed (implemented curriculum). The statistical analysis of the test results confirmed the second hypothesis of this work. "The knowledge of future experts in the field of the protection of population will have, from the point of view of the role of the complementarity principle in their preparation, a theoretical division which will be close to the normal division." By confirming this hypothesis, the correctness and applicability of the curriculum process were confirmed as it was assumed by the first hypothesis: "Using the stages of a curriculum process, an educational basis of the role of the complementarity principle can be created within a quantitative research." The contributions of this work can be summarized by following points: 1) The use of an educational text in the preparation of experts in the field of the protection of population (a practical contribution of this diploma thesis). 2) The improvement of the applicability of the theory of the curriculum process in the field of the protection of population which has not been researched so far (the improvement of the theory of the curriculum process). 3) The definition of the link of the physical aspect of the complementarity principle to the general form of this principle (the theoretical contribution of this diploma thesis).
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Nigrini, Jacques. "Kenosis and identities: pneumatological pointers." Thesis, 2006. http://hdl.handle.net/10500/1324.
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In the thesis a methodology of understanding and explicating Christian faith consistent with the mystery of the simultaneous close connection and radical difference of God, human beings and the physical-organic cosmos environment is been mapped out. The theanthropocosmic principle as an expression of the mystery functions as the heuristic key in opening up the notion of kenosis (and incarnation) of Jesus Christ and the Holy Spirit within the scope of the enduring interaction of . The Spirit in the kenotic sense of the word connects and differentiates the overall processes of being and becoming, here and there, now and then of the mystery of the `presences' of God, human beings and the natural cosmic world in being there (Dasein), being thus and thus (Sosein) and being dynamically actual (Aktsein). God acts in terms of the Spirit's operational kenotic presence within the margins of the creatureliness of people and the natural cosmic world as the kenotic clothing of God. A dynamic interpretation of the integral and differential character of being and becoming suggests that making sense of the dynamics of the formation of identities and identification is an ever ongoing endeavour. It implies a continuous process of negotiation whilst experiencing various continuums, remaining open-ended in an ever-increasing sense of wonder and mystery of "exitus a Deo-reditus in Deum".Systematic Theology and theological Ethics
D. Th. (Systematic Theology)